高等微积分

所属分类:数学  
出版时间:2009-11   出版时间:清华大学出版社   作者:David M. Bressoud   页数:386  
Tag标签:数学,Mathematics,分析,微积分  

内容概要

  本书是本科生的微积分教学用书,主要内容为:牛顿运动学基本定律(开篇),向量代数,天体力学简介,线性变换,微分形式和微分演算,隐函数反函数定理,重积分演算,曲线曲面积分,微积分基本定理,经典场论基本定理,爱因斯坦狭义相对论简介。本书特别注意数学与物理、力学等自然科学的内在联系和应用。作者在理念导引、内容选择、程度深浅、适用范围等方面都有相当周密的考虑。从我们国内重点大学的教学角度看,本书的难易程度与物理、力学和电类专业数学课的微积分相当,而思想内容则要深刻和生动些,因此适于用作这些专业本科生的教科书或学习参考书。
  

书籍目录

preface xi
1 f = ma1
 1.1 prelude to newton's principia 1
 1.2 equal area in equal time 5
 1.3 the law of gravity 9
 1.4 exercises16
 1.5 reprise with calculus 18
 1.6 exercises26
2 vector algebra 29
 2.1 basic notions29
 2.2 the dot product 34
 2.3 the cross product39
 2.4 using vector algebra 46
 2.5 exercises 50
3 celestial mechanics 53
 3.1 the calculus of curves 53
 3.2 exercises05
 3.3 orbital mechanics 06
 3.4 exercises75
4 differential forms 77
 4.1 some history77
 4.2 differential 1-forms 79
 4.3 exercises 86
 4.4 constant differential 2-forms 89
 4.5 exercises 96
 4.6 constant differential k-forms 99
 4.7 prospects 105
 4.8 exercises 107
5 line integrals, multiple integrals 111
 5.1 the riemann integral 111
 5.2 linelntegrals.113
 5.3 exercises llo
 5.4 multiple- -integrals 120
 5.5 using multiple integrals 131
 5.6 exercises
6 linear transformations 139
 6.1 basicnotions.139
 0.2 determinants 146
 6.3 history and comments 157
 6.4 exercises 158
 6.5 invertibility 165
 6.6 exercises
7 differential calculus 171
 7.1 limits 171
 7.2 exercises 178
 7.3 directional derivatives 181
 7.4 the derivative 187
 7.5 exercises 197
 7.6 the chain rule._a201
 7.7 usingthegradient.205
 7.8 exercises 207
8 integration by pullback 211
 8.1 change of variables 211
 8.2 interlude with'lagrange 213
 8.4 thesurfacelntegral 221
 8.5 heatflow228
 8.6 exercises 230
9 techniques of differential calculus 233
 9.1 implicitdifferentiation 233
 9.2 invertibility 238
 9 3 exercises 244
 9.4 locating extrema 248
 9.5 taylor's formula in several variables 254
 9.6 exercises 262
 9.7 lagrangemultipliers266
 9 8 exercises277
10 the fundamental theorem of calculus 279
 10.1 overview 279
 10.2 independence of path 286
 10.3 exercises 294
 10.4 the divergence theorems 297
 10.5 exercises 310
 10.6 stokes' theorem 314
 10.7 summary for r3 321
 10.8 exercises 323
 10.9 potential theory 326
11 e = mc2 333
 11.2 flow in space-time 338
 11.3 electromagnetic potential 345
 11.4 exercises 349
 11.5 specialrelativity 352
 11.6 exercises 360
appendices
 a an opportunity missed 361
 b bibliography365
 c clues and solutions367
index 382

章节摘录

  1.1
Prelude
to
Newton's
Principia  Popular
mathematical
history
attributes
to
Isaac
Newton
(1642-1727)
andGottfried
Wilhelm
Leibniz
(1646-1716)
the
distinction
of
having
invented
calculus.
Of
course,
it
is
not
nearly
so
simple
as
that.
Techniques
for
evaluating
areas
and
volumes
as
limits
of
computable
quantities
go
back
to
theGreeks
of
the
classical
era.
The
rules
for
differentiating
polynomials
and
theuses
of
these
derivatives
were
current
before
Newton
or
Leibniz
were
born.Even
the
fundamental
theorem
of
calculus,
relating
integral
and
differentialcalculus,
was
known
to
Isaac
Barrow
(1630-1677),
Newton's
teacher.
Yetit
is
not
inappropriate
to
date
calculus
from
these
two
men
for
they
werethe
first
to
grasp
the
power
and
universal
applicability
of
the
fundamentaltheorem
of
calculus.
They
were
the
first
to
see
an
inchoate
collection
ofresults
as
the
body
of
a
single
unified
theory.  Newton's
preeminent
application
of
calculus
is
his
account
of
celestialmechanics
in
Philosophive
Naturalis
Principia
Mathematica
or
Mathematical
Principles
of
Natural
Philosophy.
Ironically,
he
makes
very
little
specificmention
of
calculus
in
it.
This
may,
in
part,
be
due
to
the
fact
that
calculuswas
still
sufficiently
new
that
he
felt
it
would
be
suspect.
In
part,
it
is
areflection
of
an
earlier
age
in
which
mathematicians
jealously
guarded
powerful
new
techniques
and
only
revealed
the
fruits
of
their
labors.  ……

图书封面

图书标签Tags

数学,Mathematics,分析,微积分


    高等微积分下载



用户评论 (总计21条)

 
 

  •        作者在序言中说这本书受两本书的启发:Tom Apostol的Calculus--作者念本科时的课本,和H. Edward的 Advanced Calculus: A Differential Forms Approach。
       我感觉这本书可称得上是“小说型”的课本,认真读它,做好习题,你会进入与Newton,Maxwell,Poincare,E.Cartan同呼吸的境界。看看这书中行列式的引入用的篇幅就知道是“用户友好”之作。
       90年代初,在天元基金赞助下,世图出了影印版“第二学年微积分”,清华社这次影印的跟世图是一个版本,窃以为叫“高等微积分”并不妥当,基本可视为“数学分析“的同义词,会吓跑本来应有的读者--理工科学生。而且清华的影印本太贵了点儿。
       陈天权教授的评价:“(该书)是作者在Pennsylvania州立大学的讲义.作者在Freeman Dyson的鼓励下写成了这本多元微积分.它的数学内容并不深,但是它与力学,电动力学及狭义相对论结合在一起讲.使得数学与物理的相互影响历历在目.”
      
      
  •     由于研究需要,印刷质量很好
  •     深入浅出~,条理还算清晰~~
  •     忘了是谁推荐的这本。包装也很好。,挺适合学习的
  •     买了也没用上。。。,隔天就收到书了!终于买到了!书是全新的
  •     买了绝对不会觉得亏本。受益匪浅!把微积分带入平民大众!,适合简单自学一下或用来做预习
  •     非常棒,同学都要买
  •     狄多涅的书,目前正在学配套的微积分教材
  •     读起来感觉清晰明了,能打好基础
  •     但是平时听闻亚马逊就不错,简单明洁
  •     也跟他的理论一样强啊。
    看不出啊。,纸张是回收纸
  •     没有折损。,名字很。。。。
  •     不错嘀!,谱方法入门的好书
  •     ~,很好的一套书
  •     对理解有很好的帮助,和我们的教材很配
  •     微积分的经典教材,以另一种方式讲述微积分
  •     主要讲的偏微分方程。,为了考研而买
  •     内容不错,内容很全。
  •     不愧为大师,题量充足
  •     快递有点慢,很专业的
  •     很划算!,陈省身先生的大作。一直对这个领域感兴趣
 

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